Question: Mia paints interior walls at a rate of $12\dfrac{\text{m}^2}{\text{h}}$. At what rate does Mia paint in $\dfrac{\text{cm}^2}{\text{min}}$ ?
Explanation: We will convert $12\,\dfrac{\text{m}^2}{\text{h}}$ to a rate in $\dfrac{\text{cm}^2}{\text{min}}$ using the following conversion rates: There are $60\text{ min}$ per $1\text{ h}$. There are $100\text{ cm}$ per $1\text{ m}$. Therefore there are $(100\text{ cm})^2=10{,}000\text{ cm}^2$ per $1\text{ m}^2$. $\begin{aligned} &\phantom{=} \dfrac{12 \text{ m}^2}{1\text{ h}} \cdot\dfrac{1\text{ h}}{60\text{ min}}\cdot\dfrac{10{,}000\text{ cm}^2}{1\text{ m}^2} \\\\ &=\dfrac{12 \cdot 1 \cdot 10{,}000\cdot \cancel{\text{m}^2}\cdot\cancel{\text{h}} \cdot \text{cm}^2}{1\cdot 60 \cdot 1 \cdot\cancel{\text{h}}\cdot \text{min} \cdot \cancel{\text{m}^2}} \\\\ &=\dfrac{120{,}000}{60}\,\dfrac{\text{cm}^2}{\text{min}} \\\\ &=2000\,\dfrac{\text{cm}^2}{\text{min}} \end{aligned}$ In conclusion, Mia paints at a rate in $\dfrac{\text{cm}^2}{\text{min}}$ of: $2000\,\dfrac{\text{cm}^2}{\text{min}}$